# Permanent Index (PI)

### Permanent Index (PI): Overview

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 PI consists of an equally weighted tri-part asset composition:

* **⅓ $AO Token**
* **⅓ $AR Token**
* **⅓ Fair Launched Ecosystem Assets (FLPs)**

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#### Foundation

The Permanent Index maintains its composition according to the following equation:

$$
PI = \frac{1}{3}AO + \frac{1}{3}AR + \frac{1}{3}\sum\_{i=1}^{n}FLP\_i
$$

Where:

$$
\begin{aligned}
AO,\ AR &= \text{fixed proportions of the total index} \\
FLP\_i &= \text{individual Fair Launched Project assets dynamically} \\
&\quad\text{selected based on market criteria}
\end{aligned}
$$

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### Mint 

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#### Overview of Key Parameters

| Notation                                         | Description                                    | Example |
| ------------------------------------------------ | ---------------------------------------------- | ------- |
| $$AO$$                                           | The $AO Token                                  | -       |
| $$AR,\ FLP\_i$$                                  | Underlying assets held by $$PI$$               | -       |
| <p><span class="math">PI</span></p><p></p>       | Current circulating supply of $Pi tokens       | 10,000  |
| <p><span class="math">V\_{\Pi}</span></p><p></p> | Total value (in $AO) of all assets held by PI  | 20,000  |
| $$AO\_{u}$$                                      | Amount of $AO delegated by a user              | 600     |
| $$AO\_{p}$$                                      | <p>Amount of $AO<br>delegated by a project</p> | 1,200   |

***

### Token Minting Mechanism (Proportional Issuance)

When $AO$ tokens are delegated to $\Pi$, they're immediately divided into three equal portions:

* One-third remains as $AO
* One-third is used to acquire $AR
* One-third is invested into selected Fair Launched Project assets ($FLP\_i$).

The amount of $\Pi$ tokens minted is proportional to the user's contribution relative to the total value of assets within the index.

**Formula (for Users):**

$$
\Pi\_{u} = \frac{AO\_{u} \times \Pi}{V\_{\Pi}}
$$

**Example:**

$$
\begin{aligned}
\text{For }AO\_{u}&=600,\quad \Pi=10{,}000,\quad V\_{\Pi}=20{,}000:\\
\Pi\_{u}&=\frac{600\times10{,}000}{20{,}000}=300
\end{aligned}
$$

*Interpretation:* A user delegating **600 AO tokens** receives **300 new $\Pi$ tokens**, reflecting their proportional share of the index's total assets.

***

### Token Minting for Fair-Launched Projects

Projects launching via Fair Launch similarly delegate $AO$ tokens, split equally into the three asset categories. Their issued tokens also maintain proportional fairness.

**Formula (for Projects):**

$$
\Pi\_{p} = \frac{AO\_{p} \times \Pi}{V\_{\Pi}}
$$

**Example:**

$$
{For } AO\_{p}=1,200,\ \Pi=10,000,\ V\_{\Pi}=20,000:\quad
\Pi\_{p}=\frac{1,200 \times 10,000}{20,000}=600
$$

$$
\Pi\_{p}=\frac{1,200 \times 10,000}{20,000}=600
$$

*Interpretation:* A project receives **600 $\Pi$ tokens** upon delegating **1,200 AO tokens**.

***